Set the oven rack to the center position and preheat to 400 degrees F.
Place the cubed potatoes in a wide, shallow, microwave safe dish. Microwave for 3-4 minutes, stirring once, until just barely fork tender. Set aside.
In a large Dutch oven or other heavy bottomed pot, heat the olive oil over medium high heat until it shimmers. Add the ground beef and onion. Cook 5-8 minutes, or until no longer pink, breaking apart and stirring as the meat cooks. Drain all but 1 Tablespoon of the grease.
Return the pot to the heat and stir in garlic, cooking for 1-2 minutes, until fragrant. Season with salt and pepper.
Sprinkle the flour over the cooked beef and stir to combine. Cook for 2 minutes, stirring constantly. Add the wine (or broth) and deglaze the pan. Add the beef broth, then bring the contents to a simmer for 2-3 minutes, stirring occasionally, until thickened. Stir in the potato, carrots and peas, and thyme. Taste and adjust the seasonings, if desired.
Pour the contents of the pot evenly into a deep 8- or 9-inch pie or casserole dish. Roll out the pie crust to 1-inch larger than your baking dish. Place the crust on top of the pot pie mixture and mold the edges into the size of the dish. Cut a few vents in the top of the crust.
Bake for 30 to 35 minutes or until golden brown and bubbling. Allow to cool for 10 minutes before serving.